We consider debiased inference on least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous and their failure may well imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the inferential procedure to remain valid.

翻译：我们考虑对逆问题最小二乘解的无偏推断，以此避免假设精确解存在。此类假设具有实质性且并非无害，当其施加于统计模型时，若假设不成立，很可能危及推断的可靠性。我们的方法允许对一种无论解是否存在均有定义的量进行推断，且在解存在时该量能与通常的估计目标一致。就工具变量而言，这意味着我们可以用结构模型来论证分析，但这些模型无需精确成立，推断程序仍能保持有效性。